Question

Find the mode of $10$ , $12$, $11$, $10$, $15$, $20$,$19$, $21$, $11$, $9$, $10$.

Answer 1

Here we will find the Mode of the given data by checking that number which is appearing most often in the series. For example, in the series $1$, $2$, $2$, $3$ and $4$ the number $2$ is appearing maximum times in respect of the rest numbers. So, the mode will be equals $2$.

Complete step-by-step solution:
Step 1: First of all, we will check how many times a number is repeating itself in the series as shown below:
$\Rightarrow$The number $9$ is repeated only one time.
$\Rightarrow$The number
$10$ is repeated three times.
$\Rightarrow$The number $11$ is repeated two times.
$\Rightarrow$The number $12$ is repeated only one time.
$\Rightarrow$The number $15$ is repeated only one time.
$\Rightarrow$The number $19$ is repeated only one time.
$\Rightarrow$The number $20$ is repeated only one time.
$\Rightarrow$The number $21$ is repeated only one time.
Step 2: As we know that the mode of the series will be equal to that number that is repeating most often. So, in the above-given data the mode will be equals to as below:
$\Rightarrow {\text{Mode}} = 10$ $\because \left( {{\text{because it is repeating three times}}} \right)$

The mode will be equal to $10$.

Note: Students should remember that if data is given with the class intervals with their respective frequency then the formula for calculating mode will be equals to as below:
${\text{Mode}} = l + \left( {\dfrac{{{f_1} - {f_0}}}{{2{f_1} - {f_0} - {f_2}}}} \right)h$ , where $l$ is the lower limit of the modal class, $h$ is the size of the class interval, ${f_1}$ is known as the frequency of the modal class, ${f_0}$ is known as the frequency of the class preceding the modal class, and ${f_2}$ is known as the frequency of the class succeeding the modal class.